Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Using homogenous weights for approximating the partial cover problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Algorithms for facility location problems with outliers
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms
Capacitated vertex covering with applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Dependent Rounding in Bipartite Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Approximation Algorithms for Partial Covering Problems
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
The t-Vertex Cover Problem: Extending the Half Integrality Framework with Budget Constraints
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
A general approach for incremental approximation and hierarchical clustering
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation algorithms for partially covering with edges
Theoretical Computer Science
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximation of partial capacitated vertex cover
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Some results on incremental vertex cover problem
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Approximation of Partial Capacitated Vertex Cover
SIAM Journal on Discrete Mathematics
A General Approach for Incremental Approximation and Hierarchical Clustering
SIAM Journal on Computing
Set cover revisited: hypergraph cover with hard capacities
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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We study the partial vertex cover problem, a generalization of the well-known vertex cover problem. Given a graph G=(V,E) and an integer s, the goal is to cover all but s edges, by picking a set of vertices with minimum weight. The problem is clearly NP-hard as it generalizes the vertex cover problem. We provide a primal-dual 2-approximation algorithm which runs in O(V log V + E) time. This represents an improvement in running time from the previously known fastest algorithm. Our technique can also be applied to a more general version of the problem. In the partial capacitated vertex cover problem each vertex u comes with a capacity ku and a weight wu. A solution consists of a function x: V →ℕ0 and an orientation of all but s edges, such that the number edges oriented toward any vertex u is at most xuku. The cost of the cover is given by ∑v∈Vxvwv. Our objective is to find a cover with minimum cost. We provide an algorithm with the same performance guarantee as for regular partial vertex cover. In this case no algorithm for the problem was known.